(1)
Probability that all are yellow =
Probability that all are orange =
Sum of the two probabilities = 0048+ 0.0288=0.0336
Thus, the probability that at least one is orange and at least one is yellow = 1-0.0336= 0.9664= 96.64 %
(2) In addition to the above, we eliminate the "1 and 4" cases.
In these cases, any of the 5 can be taken out, so we multiply by 5.
1 yellow + 4 orange =
1 orange + 4 yellow =
Sum of two probabilities = 0.2019+0.0721=0.2740
Now adding 0.0336 to this probability =0.0336+0.2740= 0.3076
Subtracting that from 1.0000 = 1-0.3076=0.6924= 69.24 %
Thus, the probability that, of the 5 balls selected at random, at least two are orange and at least two are yellow= 69.24%